Dr. J's Maths.
Where the techniques of Maths
are explained in simple terms.

Functions - Combined Exponential & Logarithmic.
Test Yourself 1.


 

Before you start the serious stuff, read the following to show how logs and exponentials can combine to make you happy!!!!

Now to the serious stuff:
General Differentiate y = ecosx

Show that if y = sinx etanx

then the derivative is

y ' = etanx(cosx + tanx secx).
  Find the coordinates of the point on the curve y = e3x where the tangent is perpendicular to the line x + 6y - 24 = 0.  
  Differentiate .  
   
 

Evaluate.

  
     
Area

The diagram above shows the curve y = loge x and the
line y = loge 4.

(i) Solve the equation loge x = loge 4. Hence write down the coordinates of the point of intersection of the two functions.

(ii) Show that the area of the shaded region is 3 u2.

(iii) Find the exact value of .
     
     
 

The diagram shows the graphs of y = loge x and the tangent to

y = loge x at the point (e, 1). The equation of the tangent is .

(i) Explain why for all positive values of x except for x = e.

(ii) Hence show that .
   
Volume

A vase can be formed by rotating the part of the curve y= loge x between
y = 0 and y = 2 about the x axis.

Find the volume of the vase in the simplest exact form.